In multichannel optical communication systems, different modulation formats may be utilized to transmit information over long distances. In digital communication systems, modulation formats use shifts in state, such as for example, a shift in the level of light power transmitted, a shift in the frequency of the light transmitted and also a shift in the phase of the light transmitted. Generally, there are three basic types of digital modulations which are used depending on the parameter selected:
ASK Modulation (Amplitude-Shift Keying). In this modulation the carrier is allowed to enter to represent bit 1, and is not transmitted to represent bit 0, digitally modulating the carrier's amplitude.
PSK Modulation (Phase-Shift Keying). The carrier is transmitted to represent 1 and the phase inverted carrier to represent 0, giving rise to a 180° phase jump in each transition from bit 1 to 0 and from 0 to 1, and for this reason it can be considered a digital modulation of the carrier phase.
FSK Modulation (Frequency-Shift Keying). An fc1 frequency carrier is transmitted to represent bit 1 and an fc2 frequency carrier to represent bit 0, being produced a digital modulation in frequency.
The wave forms of the basic types of modulation are shown in FIGS. 1 (a), 1(b) and 1 (c). FIG. 1(a) shows the modulation with amplitude changes. FIG. 1(b) shows the modulation with phase shifts. FIG. 1(c) shows a modulation with frequency shifts.
Phase Shift Keying
The Phase Shift Keying (PSK) modulation format and variations of it, are currently frequently used in military as well as commercial communication systems. The general analytic expression for PSK is described according to B. Sklar (1988) “Digital Communications: Fundamentals and Applications” (First Edition) New Jersey, Prentice Hall as:
            s      i        ⁡          (      t      )        =                              2          ⁢          E                T              ⁢          cos      ⁡              [                                            ω              o                        ⁢            t                    +                                    ϕ              i                        ⁡                          (              t              )                                      ]              ⁢                  ⁢    for    ⁢                  ⁢                                        0            ≤            t            ≤            T                                                                          i              =              1                        ,            …            ⁢                                                  ,            M                              where the phase end, φ(t), will have M discrete values, typically expressed as
                    ϕ        i            ⁡              (        t        )              =                                        2            ⁢            π            ⁢                                                  ⁢            i                    M                ⁢                                  ⁢        for        ⁢                                  ⁢        i            =      1        ,  …  ⁢          ,  M
For example, of the binary PSK (BPSK) in FIG. 1(b), M is equal to 2. The symbol E stands for power, T for temporary duration, with 0≦t≦T. In the BPSK modulation, the signal data to be transmitted are modulated in the wave phase shift, si(t), between one of these two states 0(0°) or π (180°). As can be seen in FIG. 1(b), the diagram shows one form of the typical BPSK wave with its abrupt phase shifts in the transition of symbols; if the flow of modulated data consists of an alternating sequence of ones and zeros, there would be abrupt shifts at each transition. The wave forms of the signals may be shown as vectors in a polar coordinates diagram; the length of the vector would correspond to the signal amplitude and the direction of the vector; generally speaking, M-ary, corresponds to the signal phase relative to other M−1 signals. In the specific of BPSK, the vector diagram would show the two vectors opposite to the 180° phase. The signals may decay by means of vectors in opposition to the phase called antipodal signals. We will show this vector representation afterwards when the DQPSK diagram is presented.
PSK modulation is usually used to obtain a modulation format which makes more sensitive detection mechanisms possible within the binary modulation schemes.
Below two different modulation formats are outlined and explained for which the regenerator proposed by this invention may be of application. This is done for the purpose of being able to explain with more clarity afterwards the operating of the phase regenerator described by this invention and also the transmission and receiver schemes which make up a multichannel communication system when modulation with phase shifts is used.
There are a great variety of modulation formats that use phase shifts to transmit information. In the following sections we will summarize the most modern modulation formats and on which a great many scientific articles have recently been published. These formats function through phase shifts such as Differential Phase Shift Keying (DPSK) and Differential Quadrature Phase Shift Keying (DQPSK).
Differential PSK Detection (Differential Phase Shift keying (DPSK)
The essence of PSK differential detection is that the identity of the data is referred to phase shifts between one symbol and another. The data are differentially detected examining the signal, where the transmitted signal is primarily differentially coded. In the case of DPSK modulation, the coded bit sequence, c(k), may be, generally speaking, obtained from the following two logical equations:c(k)=c(k−1)⊕m(k)orc(k)= c(k−1)⊕m(k) c(k−1)⊕m(k)where the symbol ⊕ represents a sum in module 2 and the overbar shows the logical complement. In said expressions, m(k) stands for the original sequence of data to transmit bit to bit, c(k) stands for the coded bit obtained based on the logical operations indicated by the above equations and c(k−1) refers to the coded bit obtained prior to bit c(k). Afterwards, the information from the coded signal c(k) is translated in a phase shift sequence, θ(k), where bit ‘1’ is characterized by a 180° phase shift and bit ‘0’ is characterized by a 0° phase.
It should be mentioned that the differential coding process of a band base bit sequence prior to the modulation constitutes one of the simplest forms of coding as protection against errors. The bit sequence that is transmitted through many of the communication systems may intentionally invert their value inside the channel. Many signal processing circuits cannot discern whether any of the bit values transmitted have been inverted or not. This characteristic is known as phase ambiguity. Differential coding is used as protection against this possibility.
Below, the differential coding process is outlined via a numerical example of the information bits prior to being transmitted with the DPSK format. As has already been mentioned, a differential coding system consists of an addition operation in module two as illustrated in FIG. 2, where c(k)=c(k−1)⊕m(k), is as follows: m(k), sequence of entry data; c(k), bit to bit sequence of coded bits; c(k−1), coded bit obtained prior to c(k).
The manner in which a differential coder operates is described below. We are taking into account the bit sequence shown in FIG. 3. The coding circuit described possesses one reference bit which may be ‘0’ or ‘1’ The entry bit into the system coder is added to the reference bit, forming the second bit in the sequence of coded data. This bit obtained is added to the next information bit continuing the process described in FIG. 3, such as the Charan Langton reference, “Tutorial 2—What is Differential Phase Shift Keying?”.
The decoding process performed in the receiver is the reverse of the process described above. The entering bit sequence is added together for the purpose of recreating the original data sequence as can be seen in FIG. 4. As can be seen, each bit is added to the adjacent bit that has a delay of 1 bit. On the other hand, there also are two possibilities, the bits have been correctly transmitted without producing any errors, and on the other hand, i.e., the sequence of data received has errors (containing bits whose value has been inverted along the transmission channel) as can be seen in FIG. 5.
The receiver's decoder circuit operate in the following manner, according to Charan Langton, “Tutorial 2—What is Differential Phase Shift Keying?”. for each of the two possibilities shown in FIGS. 4 and 5. FIG. 4 shows a sequence of bits received with no errors and in FIG. 5, a sequence of bits is shown that was received with errors. In both cases, the benefit of using differential coding is that it makes it possible to recover the original signal transmitted.
The application of differential coding as phase shift coder arises from obtaining the formats of differential modulation (DPSK, DQPSK . . . ). The scheme of a DPSK detector is shown in FIG. 6 with the corresponding block diagram referred to by Sklar in 1988 as: “Digital Communications: Fundamentals and Applications” First Edition, New Jersey: Prentice Hall.
There are significant differences between the DPSK detector in FIG. 6 and a coherent PSK detector. A coherent PSK detector attempts to correlate the signal phases sent with a reference signal or local oscillator. Correlating the phase of two optical signals is an extremely difficult process. In fact this synchronization of the phases of two optical signals is the main reason for which coherent detection systems have not been developed for commercial equipment phases. In the case of a DPSK detector, the reference signal is simply a delayed version of the signal previously received. In other words, during each symbol time, each symbol received is compared with the previous symbol, and the correlation or anti-correlation between them are observed (180° out of phase).
The DPSK modulation format in contrast with PSK is much less demanding that PSK given that the information is coded as a shift (or absence of shift) in the optical phase of the signal.
DPSK is directly related to the systems with high transmission rates given that the phase fluctuation between the bits of two signals are reduced.
Although non-synchronized demodulation of a PSK signal is not strictly possible because the information resides in the carrier signal phase, detection by comparison of the phase associated with DPSK reduces the problems of synchronization associated with PSK coherent systems.
Format with Quadrature Phase Shift (Quadrature Phase Shift Keying (QPSK))
Reliable behavior of a system, represented by a low probability of error, is one of the important points to bear in mind when designing a digital communication system. Another important characteristic to keep in mind is efficiency in the use of band width or spectral efficiency defined as the ratio of bit transmission between the separation between channels (or carriers) in a multichannel system.
In the Quadrature Phase-Shift Keying (QPSK) modulation format, as well as the PSK binary format, the information to transmit is contained in the signal phase that is transmitted. In particular, the carrier signal phase acquires one of the following phase values, which are spaced an equal distance apart π/4, 3π/4, 5π/4 and 7π/4 radians For these values, the signal transmitted may be defined according to Simon Haykin, “Communication systems”, 4th edition, Ed. John Wiley & Sons, pp. 311 as:
                    s        i            ⁡              (        t        )              =                                        2            ⁢            E                    T                    ⁢      cos      ⁢              (                              2            ⁢            π            ⁢                                                  ⁢                          f              c                        ⁢            t                    +                                    π              4                        ⁢                          (                                                2                  ⁢                  i                                -                1                            )                                      )              ,                              0          ≤          t          ≤          T                                                          i            =            1                    ,          2          ,          …          ⁢                                          ,          4                    where E stands for the energy by the symbol of the signal transmitted and T stands for the duration of the symbol. The carrier signal frequency fc is equal to nc/T by one fixed integer nc. Each phase value corresponds to a single pair of bits.Spatial Diagram of the QPSK Signal
By using trigonometric identities and starting with the previous equation, the energy of the signal transmitted st(t) may be redefined by the interval 0≦t≦T through the expression defined by Simon Haykin, “Communication systems”, 4th edition, Ed. John Wiley & Sons, pp. 311.
                    s        i            ⁡              (        t        )              =                                                      2              ⁢              E                        T                          ⁢                  cos          ⁡                      (                                          π                4                            ⁢                              (                                                      2                    ⁢                    i                                    -                  1                                )                                      )                          ⁢                  cos          ⁡                      (                          2              ⁢              π              ⁢                                                          ⁢                              f                c                            ⁢              t                        )                              -                                                  2              ⁢              E                        T                          ⁢                  sin          ⁡                      (                                          π                4                            ⁢                              (                                                      2                    ⁢                    i                                    -                  1                                )                                      )                          ⁢                  sin          ⁡                      (                          2              ⁢              π              ⁢                                                          ⁢                              f                c                            ⁢              t                        )                                ,          ⁢      i    =    1    ,  2  ,  …  ⁢          ,  4
As a result of this representation two fundamental observations may be made:
There are two basic orthogonal functions between them, φ1(t) and φ2(t), contained in the expression si(t). Specifically, φ1(t) and φ2(t) are defined by a pair of carriers in quadrature, as referenced by Simon Haykin, “Communication systems”, 4th edition, Ed. John Wiley & Sons, pp. 311
                                                        ϕ              1                        ⁡                          (              t              )                                =                                                                      2                  ⁢                  E                                T                                      ⁢            cos            ⁢                          (                              2                ⁢                π                ⁢                                                                  ⁢                                  f                  c                                ⁢                t                            )                                      ,                  0          ≤          t          ≤          T                                                                            ϕ              2                        ⁡                          (              t              )                                =                                                                      2                  ⁢                  E                                T                                      ⁢                          sin              ⁡                              (                                  2                  ⁢                  π                  ⁢                                                                          ⁢                                      f                    c                                    ⁢                  t                                )                                                    ,                  0          ≤          t          ≤          T                                    There are four points of information, which are associated with the signal vectors defined according to Simon Haykin, “Communication systems”, 4th edition, Ed. John Wiley & Sons, pp. 311 as:        
                    s        i            ⁡              (        t        )              =          [                                                                  E                            ⁢                              cos                ⁡                                  (                                                            π                      4                                        ⁢                                          (                                                                        2                          ⁢                          ⅈ                                                -                        1                                            )                                                        )                                                                                                                        -                                  E                                            ⁢                              sin                ⁡                                  (                                                            π                      4                                        ⁢                                          (                                                                        2                          ⁢                          ⅈ                                                -                        1                                            )                                                        )                                                                        ]        ,      i    =    1    ,  2  ,  …  ⁢          ,  4
The QPSK format has constellations of two sizes (N=2) and four points of information (M=4). The phase angles of which increase in direction exactly as shown in FIG. 7 according to Simon Haykin, “Communication systems”, 4th edition, Ed. John Wiley & Sons, pp. 311.
Like the PSK modulation format, the QPSK possesses a minimum average power.
Differential Quadrature Phase Format Known as DQPSK which is the English Acronym for Differential Quadrature Phase Shift Keying
Given that this modulation format constitutes the basis of the research, analysis, and comparison in this invention, the details of the R(ZH)N-DQPSK, described by O. Vassilieva, et al in “Non-Linear Tolerant and Spectrally Efficient 86 Gbit/s RZ-DQPSK Format for a System Upgrade” (OFC 2003) and by R. A. Griffin, et al “Optical differential quadrature phase-shift key (oDQPSK) for high capacity optical transmission”, in Proceedings OFC'2002, pp. 367-368), where an exhaustive description of the architecture of transmitter and receiver schemes is given.
In the DQPSK modulation format, the information is coded in the optical signal phase in such a way that the phase may take one of these four possible values: 0, π/2, π and 3π/2 radians. Each value of the phase corresponds to one pair of bits, which is the symbol rate, exactly half of the bit rate. This characteristic makes any type of DQPSK format especially interesting because the effective “bit rate” of the transmission (B) only requires the use of B/2 from the electronic symbol rate. For example, it is possible to transmit at a bit rate of 40G bit per second with electronics that work at 20G Hertz due to the fact that in each symbol (identified by a phase shift) transmitted, two bits of information are sent.
DQPSK Signal Generation and Detection
In DQPSK modulation format, as in the DPSK format, it is necessary to precode the data in the transmitter to be able to use a simple and direct detection in the receiver. In the case of DQPSK, the necessary precoding function involves the implementation of a logical digital circuit which is considerably more complex than that associated with DPSK. Given that this is a multiphase modulation, with four different phase levels, the precoding function will posses two binary data entries, which will facilitate two outputs with the data that is already coded as described by R. A. Griffin, et al “Optical differential quadrature phase-shift key (ODQPSK) for high capacity optical transmission”, in Proceedings OFC'2002, pp. 367-368).
Power Spectrum of the RZ-DQPSK Signals
The spectrum of an RZ-DQPSK at the output of a transmission system, as well as its corresponding electrical signal in the receiver, may be observed in FIGS. 8(a) and 8(b) respectively.
In FIG. 8(a) we see that the band width occupied by the modulated signal is extremely width. The majority of high capacity optical systems are based on multiplexation in the wavelength to be able to obtain greater transmission rates, wavelength division multiplexing (multiplexing by division of the wavelength). In this way, due to the necessity of multiplexing various channels in the same optical link, each of these needs to be limited in bandwidth. Therefore, it is necessary to make an optical filtration. This optical filtration is carried out in the multiplexors or demultiplexers of an optical system in such a way that the interference of a channel on the others is minimized until it complies with the requirements for interference between channels.
This optical filtration, causes transitory responses due to phase shifts in the modulated signal exactly as shown in FIG. 8(b). These transitory responses, in phase as well as in power, deteriorate the reconstruction of the information at the output of the system limiting in this way the maximum capacity of transmission for distance in any given link. The main purpose of the signal regenerator for differential phase signals, presented in this invention, is to mitigate the effect of these transitory responses making a greater transmission capacity possible for the same or greater transmission distance for the same or greater capacity.
It is important to mention that U.S. Pat. No. 6,323,979, describes a regenerator that uses optical phase modulation, using solutions, in a fiber optic transmission system, in which the signal is modulated by a clock. There are many differences regarding this invention, in fact, they are completely different. Note that the modulation format in number U.S. Pat. No. 6,323,979 is by phase distribution, using the sending of solutions, the phase difference between the information contained in the solution and the signal clock to synchronize the clock in the receiver. These details show that the patent is very different from ours.